Abstract
The predictions of the frequency-domain standard diffusion equation (SDE) model for light propagation in an infinite turbid medium diverge from the more complete approximation to the linear Boltzmann transport equation at intensity modulation frequencies greater than several hundred MHz. The approximation is based on keeping only the terms l=0 and l=1 in the expansion of the angular photon density in spherical harmonics, and the nomenclature approximation is used since the spherical harmonics of order l=1 can be written in terms of the first order Legendre polynomial, which is traditionally represented by the symbol . Frequency-domain data acquired in a quasi-infinite turbid medium at modulation frequencies ranging from 0.38 to 3.2 GHz using a superheterodyning microwave detection system were analyzed using expressions derived from both the aproximation equation and the SDE. This analysis shows that the approximation provides a more accurate description of the data over this range of modulation frequencies. Some researchers have claimed that the approximation predicts that a light pulse should propagate with an average speed of c/ √3 in a thick turbid medium. However, an examination of the Green’s function that we obtained from the frequency-domain approximation model indicates that a photon density wave phase velocity of c/ √3 is only asymptotically approached in a regime where the light intensity modulation frequency aproaches infinity. The Fourier transform of this frequency-domain result shows that in the time domain, the approximation predicts that only the leading edge of the pulse (i.e., the photons arriving at the detector at the earliest time) approaches a speed of c/√3. © 1996 The American Physical Society.
- Received 4 August 1995
DOI:https://doi.org/10.1103/PhysRevE.53.2307
©1996 American Physical Society